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<!DOCTYPE html> <html lang="en"> <head> <title>subPoint -- This function evaluates a polynomial or matrix at a point.</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="software for numerical algebraic geometry" href="index.html">Bertini</a> :: <a title="This function evaluates a polynomial or matrix at a point." href="_sub__Point.html">subPoint</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> <a href="___Top__Directory.html">next</a> | <a href="_store__B__M2__Files.html">previous</a> | <a href="___Top__Directory.html">forward</a> | <a href="_store__B__M2__Files.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>subPoint -- This function evaluates a polynomial or matrix at a point.</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">subPoint(f,v,p)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">f</span>, <span>a <a title="the class of all things" href="../../Macaulay2Doc/html/___Thing.html">thing</a></span>, A polynomial or a matrix.</span></li> <li><span><span class="tt">v</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, List of variables that we will be evaluated at the point.</span></li> <li><span><span class="tt">p</span>, <span>a <a title="the class of all things" href="../../Macaulay2Doc/html/___Thing.html">thing</a></span>, A point or a list of coordinates or a matrix.</span></li> </ul> </li> <li><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>: <ul> <li><span><span class="tt">M2Precision</span> (missing documentation)<!--tag: [subPoint, M2Precision]--> <span class="tt"> => </span><span class="tt">...</span>, <span>default value 53</span>, <span></span></span></li> <li><span><span class="tt">SpecifyVariables</span> (missing documentation)<!--tag: [subPoint, SpecifyVariables]--> <span class="tt"> => </span><span class="tt">...</span>, <span>default value false</span>, <span></span></span></li> <li><span><span class="tt">SubIntoCC</span> (missing documentation)<!--tag: [subPoint, SubIntoCC]--> <span class="tt"> => </span><span class="tt">...</span>, <span>default value false</span>, <span></span></span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>Evaluate f at a point.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : R=CC[x,y,z] o1 = R o1 : PolynomialRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : f=z*x+y o2 = x*z + y o2 : R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : subPoint(f,{x,y},{.1,.2}) o3 = .1z + .2 o3 : R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : subPoint(f,{x,y,z},{.1,.2,.3},SpecifyVariables=>{y}) o4 = x*z + .2 o4 : R</code></pre> </td> </tr> </table> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i5 : R=CC_200[x,y,z] o5 = R o5 : PolynomialRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : f=z*x+y o6 = x*z + y o6 : R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i7 : subPoint(f,{x,y,z},{.1,.2,.3},SubIntoCC=>true) o7 = .23 o7 : CC (of precision 53)</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i8 : subPoint(f,{x,y,z},{.1234567890123456789012345678901234567890p200, 0,1},SubIntoCC=>true,M2Precision=>200) o8 = .123456789012345678901234567890123456789 o8 : CC (of precision 200)</code></pre> </td> </tr> </table> </div> <div> <h2>Caveat</h2> <div> <p>When SubIntoCC is set to true then unset variables will be set to zero or unexpected values.</p> </div> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">subPoint</span>:</h2> <ul> <li><kbd>subPoint(Thing,List,Thing)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="This function evaluates a polynomial or matrix at a point." href="_sub__Point.html">subPoint</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function__With__Options.html">method function with options</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Bertini.m2:3788:0</span>.</p> </div> </div> </div> </body> </html>